Determining rock properties

ABSTRACT

Techniques for determining rock properties include exerting a compressive load with a test apparatus across a rock sample that includes a specified length-to-diameter ratio; measuring, with a strain gauge, a strain on the rock sample during the compressive loading; determining, based at least in part on the compressive load, a mechanical property of the rock sample; and determining, based at least in part on the measured strain and the compressive load, an elastic property of the rock sample.

TECHNICAL FIELD

This disclosure relates to determining rock properties and, moreparticularly, determining tensile strength and elastic rock propertieswith a single test.

BACKGROUND

Rock mechanical properties are important to many practical applicationsrelated to reservoir characterization and modeling. Certain rockmechanical properties may inform a geologist, engineer or driller abouttensile properties of a particular rock formation or sample. Some rockproperties are stress dependent.

SUMMARY

The present disclosure describes a rock sample test that may determineelastic and mechanical properties of the rock sample during and with asingle test. For example, in some aspects, the rock sample test may be aBrazilian test according to American Society for Testing and Materials(ASTM) Standard D3967-08 and includes a compressive test of adisc-shaped rock sample with known geometries. In some aspects, theelastic properties may be, for example, Young's modulus or Poisson'sratio, while the mechanical properties may include tensile strength,among others.

In a general implementation, a method for determining rock propertiesincludes exerting a compressive load with a test apparatus across a rocksample that includes a specified length-to-diameter ratio; measuring,with a strain gauge, a strain on the rock sample during the compressiveloading; determining, based at least in part on the compressive load, amechanical property of the rock sample; and determining, based at leastin part on the measured strain and the compressive load, an elasticproperty of the rock sample.

In an aspect combinable with the general implementation, the specifiedlength-to-diameter ratio is between 0.2 and 0.75.

In another aspect combinable with any of the previous aspects, the testapparatus includes a Brazilian test apparatus.

In another aspect combinable with any of the previous aspects, thestrain gauge is coupled to an axial surface of the rock sample.

In another aspect combinable with any of the previous aspects, measuringa strain on the rock sample during the compressive loading includesmeasuring an incremental axial strain on the rock sample during acompressive load increment with a first strain gauge; and measuring anincremental radial strain on the rock sample during the compressive loadincrement with a second strain gauge.

In another aspect combinable with any of the previous aspects,determining, based at least in part on the measured strain and thecompressive load, the elastic property of the rock sample includesdetermining a first coefficient based at least in part on the diameterof the rock sample, the length of the rock sample, and an effectivelength of the first and second strain gauges; determining a secondcoefficient based at least in part on the diameter of the rock sample,the length of the rock sample, and the effective length of the first andsecond strain gauges; and determining the elastic property of the rocksample based at least in part on the measured incremental axial andradial strains on the rock sample, the first and second coefficients,and the compressive loading increment.

In another aspect combinable with any of the previous aspects,determining, based at least in part on the measured strain and thecompressive load, the elastic property of the rock sample includesdetermining a Young's modulus of the rock sample based on at least oneof

$\begin{matrix}{{E = {\frac{\Delta \; P}{{\Delta ɛ}_{x}}\left( {{- F} + {vG}} \right)}},} & (i)\end{matrix}$

where E is stress dependent Young's modulus of the rock sample, ΔP is acompressive loading increment, Δε_(x) is an incremental radial strain, uis Poisson's ratio of the rock sample, F is a first coefficient, and Gis a second coefficient; or

$\begin{matrix}{{E = {\frac{P}{ɛ_{x}}\left( {{- F} + {vG}} \right)}},} & ({ii})\end{matrix}$

where E is Young's modulus of the rock sample, P is a particularcompressive load, ε_(x) is a radial strain at the particular compressiveload, ν is Poisson's ratio of the rock sample, F is the firstcoefficient, and G is the second coefficient.

In another aspect combinable with any of the previous aspects,determining, based at least in part on the measured strain and thecompressive load, the elastic property of the rock sample includesdetermining Poisson's ratio of the rock sample based on at least one of

$\begin{matrix}{{\upsilon = \frac{{\left( \frac{{\Delta ɛ}_{x}}{{\Delta ɛ}_{y}} \right)G} + F}{{\left( \frac{{\Delta ɛ}_{x}}{{\Delta ɛ}_{y}} \right)F} + G}},} & (i)\end{matrix}$

where ν is stress dependent Poisson's ratio of the rock sample, Δε_(x)is an incremental radial strain, Δε_(y) is an incremental axial strain,F is a first coefficient, and G is a second coefficient; or

$\begin{matrix}{{\upsilon = \frac{{\left( \frac{ɛ_{x}}{ɛ_{y}} \right)G} + F}{{\left( \frac{ɛ_{x}}{ɛ_{y}} \right)F} + G}},} & ({ii})\end{matrix}$

where u is Poisson's ratio of the rock sample, ε_(x) is a radial strainat a particular compressive load on the rock sample, Δε_(y) is an axialstrain at the particular compressive load on the rock sample, F is thefirst coefficient, and G is the second coefficient.

In another aspect combinable with any of the previous aspects, themechanical property includes at least one of a tensile strength or abrittleness of the rock sample.

In another aspect combinable with any of the previous aspects, thestrain gauge includes a linear variable differential transformer (LVDT).

In another general implementation, a rock property test system includesa load cell configured to exert a compressive load across a rock sample;at least one strain gauge positioned to measure a strain on the rocksample during the compressive loading; and a control system communicablycoupled to the load cell and the at least one strain gauge andconfigured to perform operations including: controlling the load cell toexert an incremental compressive load on the rock sample; receiving ameasured strain on the rock sample, based on the incremental compressiveload, from the at least one strain gauge; determining, based at least inpart on the incremental compressive load, a mechanical property of therock sample; and determining, based at least in part on the measuredstrain and the incremental compressive load, an elastic property of therock sample.

In an aspect combinable with the general implementation, the rock sampleincludes a length-to-diameter ratio between 0.2 and 0.75.

In another aspect combinable with any of the previous aspects, the loadcell includes a Brazilian test apparatus.

In another aspect combinable with any of the previous aspects, thestrain gauge is configured to attach to an axial surface of the rocksample.

In another aspect combinable with any of the previous aspects, thestrain gauge includes a first strain gauge configured to measure anincremental axial strain on the rock sample during the incrementalcompressive load; and a second strain gauge configured to measure anincremental radial strain on the rock sample during the incrementalcompressive load.

In another aspect combinable with any of the previous aspects, thecontrol system is configured to perform further operations includingdetermining a first coefficient based at least in part on the diameterof the rock sample, the length of the rock sample, and an effectivelength of the first and second strain gauges; determining a secondcoefficient based at least in part on the diameter of the rock sample,the length of the rock sample, and the effective length of the first andsecond strain gauges; and determining the elastic property of the rocksample based at least in part on the measured incremental axial andradial strains on the rock sample, the first and second coefficients,and the incremental compressive load.

In another aspect combinable with any of the previous aspects, theoperation of determining, based at least in part on the measured strainand the compressive load, the elastic property of the rock sampleincludes determining a Young's modulus of the rock sample based on atleast one of

$\begin{matrix}{{E = {\frac{\Delta \; P}{{\Delta ɛ}_{x}}\left( {{- F} + {vG}} \right)}},} & (i)\end{matrix}$

where t is stress dependent Young's modulus of the rock sample, ΔP is acompressive loading increment, Δε_(x) is an incremental radial strain, νis Poisson's ratio of the rock sample, F is a first coefficient, and Gis a second coefficient; or

$\begin{matrix}{{E = {\frac{P}{ɛ_{x}}\left( {{- F} + {vG}} \right)}},} & ({ii})\end{matrix}$

where E is Young's modulus of the rock sample, P is a particularcompressive load, ε_(x) is a radial strain at the particular compressiveload, u is Poisson's ratio of the rock sample, F is the firstcoefficient, and G is the second coefficient.

In another aspect combinable with any of the previous aspects, theoperation of determining, based at least in part on the measured strainand the compressive load, the elastic property of the rock sampleincludes determining Poisson's ratio of the rock sample based on atleast one of

$\begin{matrix}{{\upsilon = \frac{{\left( \frac{{\Delta ɛ}_{x}}{{\Delta ɛ}_{y}} \right)G} + F}{{\left( \frac{{\Delta ɛ}_{x}}{{\Delta ɛ}_{y}} \right)F} + G}},} & (i)\end{matrix}$

where ν is stress dependent Poisson's ratio of the rock sample, Δε_(x)is an incremental radial strain, AE_(y) is an incremental axial strain,F is a first coefficient, and G is a second coefficient; or

$\begin{matrix}{{\upsilon = \frac{{\left( \frac{ɛ_{x}}{ɛ_{y}} \right)G} + F}{{\left( \frac{ɛ_{x}}{ɛ_{y}} \right)F} + G}},} & ({ii})\end{matrix}$

where ν is Poisson's ratio of the rock sample, ε_(x) is a radial strainat a particular compressive load on the rock sample, Δε_(y) is an axialstrain at the particular compressive load on the rock sample, F is thefirst coefficient, and G is the second coefficient..

In another aspect combinable with any of the previous aspects, themechanical property includes at least one of a tensile strength or abrittleness of the rock sample.

In another general implementation, a method includes performing aBrazilian test on a rock sample, the Brazilian test including exertingan incremental compressive load across a rock sample, and determining,based at least in part on the incremental compressive load, a mechanicalproperty of the rock sample; measuring, with a strain gauge, a strain onthe rock sample during the incremental compressive load; anddetermining, based at least in part on the measured strain and theincremental compressive load, an elastic property of the rock sample.

In an aspect combinable with the general implementation, the rock sampleincludes a disc having a length-to-diameter ratio between 0.2 and 0.75.

In another aspect combinable with any of the previous aspects, thestrain includes an axial strain and a radial strain, and determining theelastic property of the rock sample includes determining the elasticproperty of the rock sample based at least in part on the axial andradial strains on the rock sample and the incremental compressive load.

In another aspect combinable with any of the previous aspects,determining the elastic property of the rock sample based at least inpart on the axial and radial strains on the rock sample and theincremental compressive load includes determining the elastic propertyof the rock sample based at least in part on the axial and radialstrains on the rock sample, the incremental compressive load, and twopredetermined constants.

In another aspect combinable with any of the previous aspects, the twopredetermined constants are based at least in part on a diameter of therock sample, a length of the rock sample, and an effective length of thestrain gauge.

Implementations according to the present disclosure may include one ormore of the following features. For example, tensile and elasticparameters of a rock sample can be estimated in a single compressiontest, such as a Brazilian test. As another example, tensile and elasticproperties of a rock sample may be determined by a widely-accepted andused test procedure, for example, the Brazilian test procedure. As yetanother example, implementations described in the present disclosure mayminimize the requirement of multiple core samples to determine tensileand elastic properties. For example, implementations may determine, in asingle test, a tensile strength, a Young's modulus, a Poisson's ratio, astress-strain curve, brittleness and toughness of a rock sample.Further, implementations may allow for core samples to be tested thathave a range of diameters. As another example, numerical inversions arenot required for testing the rock sample to determine tensile andelastic properties, and thus may be easier to implement in practicalapplications. As another example, the described implementations do notrequire any extra mechanical testing equipment and can be incorporatedin conventional compression test equipment.

The details of one or more implementations of the subject matterdescribed in this disclosure are set forth in the accompanying drawingsand the description. Other features, aspects, and advantages of thesubject matter will become apparent from the description, the drawings,and the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic illustration of a testing apparatus fordetermining one or more rock mechanical properties according to thepresent disclosure.

FIG. 2A-2C are schematic illustrations of several example loadingassemblies of a test apparatus for determining one or more rockmechanical properties according to the present disclosure.

FIG. 3 is a schematic illustration of a rock sample according to thepresent disclosure.

FIGS. 4A-4B are schematic illustrations of a rock sample that include atleast one strain gauge according to the present disclosure.

FIG. 5 is a graph that illustrates Young's modulus of a rock sampleduring testing according to the present disclosure.

FIG. 6 is a graph that illustrates stress-strain curve and Poisson'sratio of a rock sample during testing according to the presentdisclosure.

FIG. 7 is a numerical model of a rock sample that is determined during arock sample test simulation according to the present disclosure.

FIGS. 8 and 9 are numerical models of vertical and horizontal stresscontours, respectively, of a rock sample that are determined during arock sample test simulation according to the present disclosure.

FIG. 10 is a graph that illustrates normalized Young's modulus andPoisson's ratio of a rock sample that are determined during a rocksample test simulation according to the present disclosure.

FIG. 11 is a schematic illustration of an example controller of atesting apparatus for determining one or more rock mechanical propertiesaccording to the present disclosure.

DETAILED DESCRIPTION

The present disclosure describes a rock sample test that may determineelastic and mechanical properties of the rock sample during and with asingle test. For example, in some aspects, the rock sample test may be aBrazilian test according to American Society for Testing and Materials(ASTM) Standard D3967-08 and includes a compressive test of adisc-shaped rock sample with known geometries. In some aspects, theelastic properties may be, for example, Young's modulus or Poisson'sratio, while the mechanical properties may include tensile strength,among others.

FIG. 1 is a schematic illustration of a testing apparatus 100 fordetermining one or more rock mechanical properties. Testing apparatus100, generally may be operated to perform compressive tests, includingindirect tensile strength test, or a splitting test, on a rock sample(for example, an isotropic rock sample or an anisotropic rock sample),such as the rock sample 130 shown in FIG. 1. For example, in someimplementations, the testing apparatus 100 may perform a Brazilian teston the rock sample 130. The Brazilian test, for example, is a laboratorytest for indirect measurement of tensile strength of the rock sample 130or other hardened material (for example, concrete, cement). Generally,in the Brazilian test, a disc-shaped rock sample (rock sample 130) isloaded by two opposing platens in contact with opposed portions of aradial surface of the rock sample 130. A compressive load isincrementally increased on the rock sample 130 until the rock sample 130fails (in other words, splits), after which, mechanical properties ofthe rock sample (for example, tensile strength, brittleness) may becalculated or determined. Testing criteria such as increment of load,rate of loading, for instance, may be adjusted from test to test.

The example implementation of the testing apparatus 100, which may alsobe referred to in this disclosure as a Brazilian test apparatus,includes a load frame 105 positioned on a base 110 and arranged tosupport load cells 115. The illustrated load cells 115 are positionedsuch that an upper platen 120 and a lower platen 125 are mounted inbetween the cells 115. The upper platen 120 and the lower platen 125 areseparated, during non-operation of the testing apparatus 100, to allowthe rock sample 130 to be placed between the platens 120 and 125. Whenin non-compressive contact with the platens 120 and 125, a radialsurface of the rock sample 130 is in contact with the upper and lowerplatens 120 and 125, respectively. Thus, in FIG. 1, an axial surface,defined by a diameter of the rock sample 130, is perpendicular to thecontacting surfaces of the platens 120 and 125 (in other words, thesurfaces of the platens 120 and 125 that contact the radial surface ofthe rock sample 130).

In the illustrated implementation, one or more strain gauges 135 areshown as engaged (for example, with adhesive) with the axial surface ofthe rock sample 130. The one or more strain gauges 135, generally, maybe any device that measures strain on the rock sample 130 during acompressive loading operation. The strain gauge 130, for example, may bea linear variable differential transformer (LVDT) or other strain gaugethat measures strain based on an electrical conductance of a deformableelectrical conductor. In some implementations, two strain gauges 135 maybe attached to the rock sample 130 to measure axial and radial strain,respectively.

The testing apparatus 100, as shown, includes a control system 140.Although shown separately from the load cells 115 and other portions ofthe testing apparatus 100, the control system 140 may be built into, orintegrated with, the testing apparatus 100. In any event, the controlapparatus 140 may be communicably coupled to one or more components ofthe testing apparatus 100, such as the load cells 115, and the straingauge(s) 135. The control system 140, generally, may control operationof the load cells 115 (for example, rate of loading, loading compressiveforce) to exert a compressive load on the rock sample 130. The controlsystem 140 may also receive data from, for example, the load cells 115(compressive load values, travel distance of the platens 120 and 125during loading) and the strain gauge(s) 135 (for example, measured axialand radial strain on the rock sample 130). The control system 140 may bea microprocessor based controller, an electrical or electromechanicalbased controller, a pneumatic or hydraulic based controller.

Turning briefly to FIGS. 2A-2C, schematic illustrations of severalexample loading assemblies of the test apparatus 100 are illustrated. Asshown, each platen (upper platen 120 and lower platen 125) includes asubstantially planar or flat contact surface 122 to hold the rock sample130 in between. Example loading assembly 200 in FIG. 2A includesseparators 215 that are positioned between the contact surfaces 122 andthe radial surface of the rock sample 130. The separators 215 may berigid or pliable, such as cushions. During operation of the testingapparatus 100, a compressive load is transferred from the platens 120and 125, through the separators 215, and to the rock sample 130.

Example loading assembly 205 in FIG. 2B includes no barriers between thecontact surfaces 122 and the radial surface of the rock sample 130.Thus, during operation of the test apparatus 100, a compressive load istransferred from the platens 120 and 125 directly to the rock sample130.

Example loading assembly 210 in FIG. 2C includes a rod 220 (for example,a steel or other rigid rod) is positioned between each contact surface122 and the radial surface of the rock sample 130. During operation ofthe testing apparatus 100, a compressive load is transferred from theplatens 120 and 125, through the rods 220, and to the rock sample 130.

FIG. 3 is a schematic illustration of the rock sample 130. As shown, therock sample 130 has a diameter 250 of “D” and a length 255 of “L.” Aratio of length-to-diameter of the rock sample 130 may vary; thus, therock sample 130 may have various sizes, as appropriate, for example,based on the testing apparatus 100. In some aspects, the rock sample 130may have a specified length-to-diameter ratio that conforms with theAmerican Society for Testing and Materials (ASTM) Standard D3967-08:“Standard Test Method for Splitting Tensile Strength of Intact Rock CoreSpecimens.” Under this Standard, for example, a diameter of the rocksample 130 must be at least 10 times greater than the largest mineralgrain constituent. In some implementations, therefore, alength-to-diameter ratio of the rock sample 130 confirming to thisStandard is between 0.2 and 0.75.

As shown in FIG. 3, the rock sample 130 has a radial surface 132 and twoopposed axial surfaces 134. During operation of the testing apparatus100, a compressive load 260 (labeled “P” in this figure) is exerted onthe radial surface 132 of the rock sample, through the platens 120 and125 (which are shown in FIG. 1 and FIGS. 2A-2C).

FIGS. 4A-4B are schematic illustrations of the rock sample 130 thatincludes at least one strain gauge. In FIG. 4A, a strain gauge 275 isattached (for example, with adhesive) to the rock sample 130 at a centerpoint 270 of an axial face of the sample 130. The strain gauge 275, inFIG. 4A, may be an axial strain gauge that measures an axial strain (forexample, strain along an x-axis, as shown in FIG. 3) during compressiveloading of the rock sample 130. In FIG. 4B, a strain gauge 280 isattached (for example, with adhesive) to the rock sample 130 at thecenter point 270 of the axial face of the sample 130. The strain gauge280, in FIG. 4B, may be a radial strain gauge that measures a radialstrain (for example, strain along a y-axis, as shown in FIG. 3) duringcompressive loading of the rock sample 130. Although each strain gauge275 and 280 is illustrated as attached independently to the rock sample130, in some implementations, the two strain gauges (275 and 280) areboth attached to the rock sample 130, so that both axial and radialstrain on the rock sample 130 may be measured during compressive loading(for example, during a Brazilian test of the rock sample 130 using thetesting apparatus 100).

Thus, during an example operation of the testing apparatus 130, thecompressive load, P, is known, as is the diameter, D, and length, L, ofthe rock sample 130. Also known is an effective length, 2 l of thestrain gauges 275 and 280 (which, in some implementations, isidentical). In the example operation, P is measured in Newtons (N), andD, L, and 2 l are measured in millimeters (mm). Thus, for rock sample130 (for example, an isotropic or anisotropic sample), the stress statefor the sample 130 may be determined according to Equations (1) to (3):

$\begin{matrix}{\sigma_{x} = {\frac{2P}{\pi \; L}\left\{ {\frac{\left( {\left( \frac{D}{2} \right) - y} \right)x^{2}}{\left( {\left( {\left( \frac{D}{2} \right) - y} \right)^{2} + x^{2}} \right)^{2}} + \frac{\left( {\left( \frac{D}{2} \right) + y} \right)x^{2}}{\left( {\left( {\left( \frac{D}{2} \right) + y} \right)^{2} + x^{2}} \right)^{2}} - \frac{1}{D}} \right\}}} & {{Eq}.\mspace{11mu} 1} \\{\sigma_{y} = {\frac{2P}{\pi \; L}\left\{ {\frac{\left( {\left( \frac{D}{2} \right) - y} \right)^{3}}{\left( {\left( {\left( \frac{D}{2} \right) - y} \right)^{2} + x^{2}} \right)^{2}} + \frac{\left( {\left( \frac{D}{2} \right) + y} \right)^{3}}{\left( {\left( {\left( \frac{D}{2} \right) + y} \right)^{2} + x^{2}} \right)^{2}} - \frac{1}{D}} \right\}}} & {{Eq}.\mspace{11mu} 2} \\{\tau_{xy} = {\frac{2P}{\pi \; L}\left\{ {\frac{\left( {\left( \frac{D}{2} \right) - y} \right)^{2}x}{\left( {\left( {\left( \frac{D}{2} \right) - y} \right)^{2} + x^{2}} \right)^{2}} + \frac{\left( {\left( \frac{D}{2} \right) + y} \right)^{2}x}{\left( {\left( {\left( \frac{D}{2} \right) + y} \right)^{2} + x^{2}} \right)^{2}}} \right\}}} & {{Eq}.\mspace{11mu} 3}\end{matrix}$

In Equations (1) to (3), σ_(x) is a normal stress along the x-axis ofthe rock sample 130 (as shown in FIG. 3), σ_(y) is a normal stress alongthe y-axis of the rock sample 130 (as shown in FIG. 2B), and τ_(xy) is ashear stress. Each stress has units of mega Pascals (MPa).

Because the effective length of the strain gauges 275 and 280 is known,as well as the diameter of the rock sample 130, two constantcoefficients, A and B, may be developed based on the geometry of thestrain gauges 275 and 280, according to Equations (4) and (5):

$\begin{matrix}{A = \left( {\frac{D}{2} - l} \right)} & {{Eq}.\mspace{11mu} 4} \\{B = \left( {\frac{D}{2} + l} \right)} & {{Eq}.\mspace{11mu} 5}\end{matrix}$

Based on Equations (1) to (5), the following equations for an averagevalue of the normal stress, σ_(x) (along a side boundary of strain gauge275) and σ_(y) (along a top boundary of the strain gauge 280) can beexpressed as:

$\begin{matrix}{{\overset{\_}{\sigma}}_{x} = {\frac{1}{l}{\int_{0}^{l}{{\frac{2P}{\pi \; L}\left\lbrack {\frac{\left( {\left( \frac{D}{2} \right) - y} \right)l^{2}}{\left( {\left( {\left( \frac{D}{2} \right) - y} \right) + l^{2}} \right)^{2}} + \frac{\left( {\left( \frac{D}{2} \right) + y} \right)l^{2}}{\left( {\left( {\left( \frac{D}{2} \right) + y} \right) + l^{2}} \right)^{2}} - \frac{1}{D}} \right\rbrack}{dy}}}}} & {{Eq}.\mspace{11mu} 6} \\{{\overset{\_}{\sigma}}_{y} = {\frac{1}{l}{\int_{0}^{l}{{\frac{2P}{\pi \; L}\left\lbrack {\frac{A^{3}}{\left( {A^{2} + x^{2}} \right)^{2}} + \frac{B^{3}}{\left( {B^{2} + x^{2}} \right)^{2}} - \frac{1}{D}} \right\rbrack}{dx}}}}} & {{Eq}.\mspace{11mu} 7}\end{matrix}$

Equations (6) and (7) can then be integrated to produce the followingequations for the average values of the normal stress, σ_(x) and σ_(y) .

$\begin{matrix}{{\overset{\_}{\sigma}}_{x} = {\frac{P}{l\; \pi \; L}\left\lbrack {{l^{2}\left( {\frac{1}{A^{2} + l^{2}} - \frac{1}{B^{2} + l^{2}}} \right)} - \frac{2l}{D}} \right\rbrack}} & {{Eq}.\mspace{11mu} 8} \\{{\overset{\_}{\sigma}}_{y} = {\frac{2P}{l\; \pi \; L}\left\{ {{\frac{A^{3}}{2}\left\lbrack {{\frac{1}{A^{3}}\arctan \frac{l}{A}} + \frac{l}{A^{2}\left( {l^{2} + A^{2}} \right)}} \right\rbrack} + {\frac{B^{3}}{2}\left\lbrack {{\frac{1}{B^{3}}\arctan \frac{l}{B}} + \frac{l}{B^{2}\left( {l^{2} + B^{2}} \right)}} \right\rbrack} - \frac{l}{D}} \right\}}} & {{Eq}.\mspace{11mu} 9}\end{matrix}$

Based on Equations (8) and (9), two coefficients may be developed basedon the strain gauge and rock sample geometry (for example, effectivelength of the strain gauges 275/280 and diameter and length of the rocksample 130). These coefficients, F and G, may be expressed according toEquations (10) and (11):

$\begin{matrix}{F = {\frac{1}{l\; \pi \; L}\left( {{l^{2}\left( {\frac{1}{A^{2} + l^{2}} - \frac{1}{B^{2} + l^{2}}} \right)} - \frac{2l}{D}} \right\rbrack}} & {{Eq}.\mspace{11mu} 10} \\{G = {\frac{1}{l\; \pi \; L}\left\{ {{A^{3}\left\lbrack {{\frac{1}{A^{3}}\arctan \frac{l}{A}} + \frac{l}{A^{2}\left( {l^{2} + A^{2}} \right)}} \right\rbrack} + {B^{3}\left\lbrack {{\frac{1}{B^{3}}\arctan \frac{l}{B}} + \frac{l}{B^{2}\left( {l^{2} + B^{2}} \right)}} \right\rbrack} - \frac{2l}{D}} \right\}}} & {{Eq}.\mspace{11mu} 11}\end{matrix}$

Thus, both F and G are constant coefficients related to D, L and 2 l,and Equations (8) and (9) can be simplified as:

σ _(x)=PF   Eq. 12

σ _(y)=PG Eq. 13.

According to the relationship of strain and stress, the tensile strain(ε_(x)) and compressive strain (ε_(y)) on the rock sample 130 duringcompressive loading is generated by both σ_(x) and σ_(y) according tothe following Equations (14) and (15):

$\begin{matrix}{ɛ_{x} = {\frac{1}{E}\left( {{- {\overset{\_}{\sigma}}_{x}} - {\upsilon \; {\overset{\_}{\sigma}}_{y}}} \right)}} & {{Eq}.\mspace{11mu} 14} \\{ɛ_{y} = {\frac{1}{E}\left( {{{- \upsilon}{\overset{\_}{\sigma}}_{x}} + \; {\overset{\_}{\sigma}}_{y}} \right)}} & {{Eq}.\mspace{11mu} 15}\end{matrix}$

In Equations (14) and (15), ε_(x) is the tensile, or radial, strain,ε_(y) is the compressive, or axial, strain, E is the tensile elasticmodulus, and ν is Poisson's ratio. By substituting Equations (12) and(13) into Equations (14) and (15), Equations (16) and (17) follow:

$\begin{matrix}{ɛ_{x} = {\frac{P}{E}\left( {{- F} + {\upsilon \; G}} \right)}} & {{Eq}.\mspace{11mu} 16} \\{ɛ_{y} = {\frac{P}{E}\left( {{{- \upsilon}\; F} + G} \right)}} & {{Eq}.\mspace{11mu} 17}\end{matrix}$

Therefore, the radial strain and axial strain are the function oftensile elastic modulus (Young's modulus) and Poisson's ratio of therock sample 130. According to Equations (16) and (17), Poisson's ratiois calculated as:

$\begin{matrix}{\upsilon = \frac{{\left( \frac{ɛ_{x}}{ɛ_{y}} \right)G} + F}{{\left( \frac{ɛ_{x}}{ɛ_{y}} \right)F} + G}} & {{Eq}.\mspace{11mu} 18}\end{matrix}$

By exchanging ε_(x) and E in Equation (16), the tensile elastic modulus(Young's modulus) can be formulated as:

$\begin{matrix}{E = {\frac{P}{ɛ_{x}}\left( {{- F} + {\upsilon \; G}} \right)}} & {{Eq}.\mspace{11mu} 19}\end{matrix}$

Therefore, according to Equations (18) and (19), the radial strain andaxial strain are functions of elastic mechanical properties of the rocksample 130: the tensile elastic modulus (Young's modulus) and Poisson'sratio. During operation of the testing apparatus 100 in exerting acompressive load on the rock sample 130, the radial and axial strainsare measured by the strain gauges 280 and 275, respectively. Thus, for aknown incremental compressive load exerted on the rock sample 130 by thetesting apparatus 100, the elastic properties of tensile elastic modulus(Young's modulus) and Poisson's ratio can be determined, for example, bythe control system 140. When the Young's modulus and Poisson's ratio forthe rock sample 130 are stress dependent, implementations of the presentdisclosure allow for determining the related parameters based on thesuperposition principle. Since the elastic properties are obtained fromthe linear section of stress-strain curve, the Young's modulus andPoisson's ratio can also be written as Equations (20) and (21):

$\begin{matrix}{E = {\frac{\Delta \; P}{\Delta \; ɛ_{x}}\left( {{- F} + {\upsilon \; G}} \right)}} & {{Eq}.\mspace{11mu} 20} \\{\upsilon = \frac{{\left( \frac{\Delta \; ɛ_{x}}{{\Delta ɛ}_{y}} \right)G} + F}{{\left( \frac{{\Delta ɛ}_{x}}{{\Delta ɛ}_{y}} \right)F} + G}} & {{Eq}.\mspace{11mu} 21}\end{matrix}$

Therefore, during operation of the testing apparatus 100 to test therock sample 130, both mechanical and elastic properties of the rocksample 130 can be determined with a single test (for example, a singleBrazilian test). For example, as outlined previously, the elasticproperties of Young's modulus and Poisson's ratio for each loading (P)under which strain increments are measured (by strain gauges 275 and280) can be determined for the rock sample 130. Also, the correspondingstresses can be obtained from Equations (12) and (13) for a givenloading, P.

Other mechanical properties, such as tensile strength, of the rocksample 130 may also be determined during the test. For instance, tensilestrength, σ_(t), can be determined at failure of the rock sample 130 (ata particular load, P) according to:

$\begin{matrix}{\sigma_{t} = \frac{2P}{\pi \; {DL}}} & {{Eq}.\mspace{11mu} 22}\end{matrix}$

Accordingly, an example operation with the testing apparatus includespreparing the rock sample 130 for testing, for example, according toASTM D3967-08 with a length-to-diameter ration of between 0.2 and 0.75.The strain gauges 275 and 280 are attached to the rock sample 130, whichis placed within the testing apparatus between the upper and lowerplatens 120 and 125, respectively. A compression test (for example, aBrazilian test) is conducted with the testing apparatus 100, and theincremental compressive loads (ΔP), along with resulting axial andradial strains, on the rock sample 130 are recorded (for example, by thecontrol system 140). Based on the known geometries of the rock sample130 (for example, D and L) and the known geometry of the strain gauges275 and 280 (for example, l), the aforementioned mechanical propertiesmay be determined. Mechanical properties of the rock sample 130, such astensile strength, may be calculated, as well as elastic properties, suchas Young's modulus and Poisson's ratio.

FIG. 5 is a graph 400 that illustrates a determination of Young'smodulus (E) of a rock sample during testing. For example, graph 400illustrates the results of testing on one of six rock samples accordingto the operation of testing apparatus 100 described in this disclosure.The rock samples are shale, each with dimensions of about 25.4 mmdimeter and 19.1 mm length (providing a length-to-diameter ratio ofabout 0.75). Graph 400 illustrates the results of one of the six testedsamples, and includes a y-axis 405 for axial stress (in units of MPa) ofthe rock sample and an x-axis 410 of the axial strain (in units ofmillistrain (me)) of the rock sample during compressive loadingincrements. Because Young's modulus is determined by a slope of astress-strain curve 415 over the incremental compressive loading, graph400 shows this slope to be about 3.0 GPa.

FIG. 6 is a graph 500 that illustrates a determination of Poisson'sratio (u) of a rock sample during testing based on Eq. 21. For a givenstress condition (or a given P), measured increments of strains during acompressive load increment are used to calculate Young's modulus (E) andPoisson's ratio (ν). In this way, Young's modulus (E) and Poisson'sratio (ν) are determined as functions of stress. As with graph 400,graph 500 illustrates the results of testing on one of six rock samplesaccording to the operation of testing apparatus 100 described in thisdisclosure. The rock samples are shale, each with dimensions of about25.4 mm dimeter and 19.1 mm length (providing a length-to-diameter ratioof about 0.75). Graph 500 illustrates the results of one of the sixtested samples, and includes a y-axis 505 for Poisson's ratio of therock sample and an x-axis 510 of the axial stress of the rock sampleduring compressive loading increments. As illustrated, except for someinitial loading increments, the Poisson's ratio plot 515 of the testedsample is between about 0.2 and 0.3.

FIG. 7 is a graph 600 of a numerical model 605 of a rock sample that isdetermined during a rock sample test simulation. For example, to furtherconfirm the previously described operation of the testing apparatus 100to perform a single test on a rock sample to determine elastic andmechanical properties, a numerical model was developed in FLAC®. Thenumerically modeled rock sample comprises a disc having a diameter ofabout 25.4 mm. In the legend 620 of FIG. 6, “Grid Plot” presents thecomputational mesh for simulating Brazilian disc test in a FLAC®numerical model; “Beam Plot” indicates the loading platens; “StructureVelocity” shows that the Brazilian disc is loaded by two platens at aconstant loading rate in the model.

In the model 605, the rock sample is loaded by two platens, one at thetop and the other at the bottom, in strain control mode. The simulationis stopped after the rock sample is squeezed for 0.2 mm in the vertical(axial) direction. The load, P, applied on the platens is measured as215 KN. The contour of the vertical stress distribution inside the discgiven by the numerical model 605, which compares well with theanalytical solution in Eq. (2). In these plots, the numerical solutionsare computed from FLAC® simulation; while the analytical solutions areobtained by programming closed-form solution Eq. (2) into functionsusing FISH®, a built-in programming language in FLAC®. This function isexecuted at the center of all zones in the FLAC® numerical model 605 sothat direct comparison can be made between the numerical solutions shownin FIG. 7 and analytical solutions using the previously-describedequations. As shown in FIG. 7, the numerical solution and analyticalsolution of vertical stress are substantially identical.

The strains developed along the strain gauges attached to the rocksample in the model 605 can be calculated from measurement of twosymmetric points along the x-axis and the y-axis in the model 650, forexample, the strains between and As shown in the graph 600, an axialstrain is measured by axis 610 while a radial strain is measured by axis615 (both axes have units of mm). The aforementioned strains and ‘C’-‘D’are determined as follows:

$\begin{matrix}{ɛ_{lx} = \frac{x_{d}^{B} - x_{d}^{A}}{x^{B} - x^{A}}} & {{Eq}.\mspace{11mu} 23} \\{ɛ_{ly} = \frac{y_{d}^{D} - y_{d}^{C}}{y^{D} - y^{C}}} & {{Eq}.\mspace{11mu} 24}\end{matrix}$

In Eqs. (23) and (24), x_(d) ^(A) and x_(d) ^(B) are the x-displacementat points A and B (shown in FIG. 7) which are symmetric about theorigin, and x^(A)and x^(B)are the x-coordinates at A and B (note, bothpoints are on the x-axis, so y =0). Similarly, y_(d) ^(C) and y_(d) ^(D)are the y-displacement at points C and D (shown in FIG. 7) which aresymmetric about the origin, and y^(C) and y^(D) are the y-coordinates atC and D (note, both points are on the y-axis, so x=0).

The Young's modulus and Poisson's ratio can be calculated from theapplied load on the platens and the measured strains (for example,ε_(1x) and ε_(1y)). For short strain gauges (for example, their lengthis only 1% of disc diameter), the calculated Young's modulus is 8.18 GPaand Poisson's ratio is 0.364.

FIG. 8 illustrates a graph 700 of a numerical model 705 of verticalstress contours of the rock sample that are determined during the rocksample test FLAC® simulation as described previously. FIG. 9 illustratesa graph 800 of a numerical model 805 of horizontal stress contours ofthe rock sample that are determined using the analytical solution (forexample, with Eq. (2)) as described previously. FIGS. 8 and 9, forexample, demonstrate the stress distribution within the rock sampleaccording to the FLAC® simulation. In FIG. 8, the graph 700 includes anx-axis 715 that shows displacement of the radial strain gauge (in mm),while a y-axis 710 shows displacement of the radial strain gauge (inmm). In the legend 720, “Boundary plot” marks the boundary of aBrazilian disc (the rock sample); “SYY-FLAC” shows the vertical stresscontour resulting from the vertical load of 215 KN predicted by thenumerical model in FLAC®. In FIG. 9, the graph 800 includes an x-axis815 that shows displacement of the radial strain gauge (in mm), while ay-axis 810 shows displacement of the radial strain gauge (in mm). In thelegend 820, “SYY-analytical” indicates the vertical stress contourresulting from the vertical load of 215 KN evaluated by the analyticalsolution (Eq. 2) described in this disclosure.

FIG. 10 is a graph 900 that illustrates normalized Young's modulus andPoisson's ratio of the rock sample that are determined during the rocksample test simulation in FLAC® described previously. Graph 900 includesan x-axis 910 that represents normalized strain gauge length(dimensionless) and a y-axis 905 that represents normalized values forYoung's modulus and Poisson's ratio. Calculated Young's modulus isrepresented by plot 915, while calculated Poisson's ratio is representedby plot 920. As shown by plots 915 and 920, the calculated elasticproperties of the simulated rock sample test may be dependent on thegeometric relationship between the strain gauges used to measure axialand radial strain and the rock sample disc. For example, as the lengthof the strain gauges increases, the calculated Young's modulus andPoisson's ratio decrease, as shown in graph 900. Note that the Young'smodulus is normalized by 8.18 GPa and Poisson's ratio normalized by0.364 in FIG. 10. In some aspects, therefore, the measurement of Young'smodulus and Poisson's ratio may be quite accurate if the strain gaugelength is less than 10% of the disc diameter of the rock sample.

FIG. 11 is a schematic illustration of an example controller 1000 of atesting apparatus for determining one or more rock mechanicalproperties. For example, the controller 1000 can be used for theoperations described previously, for example as or as part of thecontrol system 140 or other controllers described in this disclosure.For example, the controller 1000 may be communicably coupled with, or asa part of, one or both of a vehicle engine and on-board fuel separationsystem as described in this disclosure.

The controller 1000 is intended to include various forms of digitalcomputers, such as printed circuit boards (PCB), processors, or digitalcircuitry, that is part of a vehicle. Additionally the system caninclude portable storage media, such as, Universal Serial Bus (USB)flash drives. For example, the USB flash drives may store operatingsystems and other applications. The USB flash drives can includeinput/output components, such as a wireless transmitter or USB connectorthat may be inserted into a USB port of another computing device.

The controller 1000 includes a processor 1010, a memory 1020, a storagedevice 1030, and an input/output device 1040. Each of the components1010, 1020, 1030, and 1040 are interconnected using a system bus 1050.The processor 1010 is capable of processing instructions for executionwithin the controller 1000. The processor may be designed using any of anumber of architectures. For example, the processor 1010 may be a CISC(Complex Instruction Set Computers) processor, a RISC (ReducedInstruction Set Computer) processor, or a MISC (Minimal Instruction SetComputer) processor.

In one implementation, the processor 1010 is a single-threadedprocessor. In another implementation, the processor 1010 is amulti-threaded processor. The processor 1010 is capable of processinginstructions stored in the memory 1020 or on the storage device 1030 todisplay graphical information for a user interface on the input/outputdevice 1040.

The memory 1020 stores information within the controller 1000. In oneimplementation, the memory 1020 is a computer-readable medium. In oneimplementation, the memory 1020 is a volatile memory unit. In anotherimplementation, the memory 1020 is a non-volatile memory unit.

The storage device 1030 is capable of providing mass storage for thecontroller 1000. In one implementation, the storage device 1030 is acomputer-readable medium. In various different implementations, thestorage device 1030 may be a floppy disk device, a hard disk device, anoptical disk device, or a tape device.

The input/output device 1040 provides input/output operations for thecontroller 1000. In one implementation, the input/output device 1040includes a keyboard and/or pointing device. In another implementation,the input/output device 1040 includes a display unit for displayinggraphical user interfaces.

The features described can be implemented in digital electroniccircuitry, or in computer hardware, firmware, software, or incombinations of them. The apparatus can be implemented in a computerprogram product tangibly embodied in an information carrier, forexample, in a machine-readable storage device for execution by aprogrammable processor; and method steps can be performed by aprogrammable processor executing a program of instructions to performfunctions of the described implementations by operating on input dataand generating output. The described features can be implementedadvantageously in one or more computer programs that are executable on aprogrammable system including at least one programmable processorcoupled to receive data and instructions from, and to transmit data andinstructions to, a data storage system, at least one input device, andat least one output device. A computer program is a set of instructionsthat can be used, directly or indirectly, in a computer to perform acertain activity or bring about a certain result. A computer program canbe written in any form of programming language, including compiled orinterpreted languages, and it can be deployed in any form, including asa stand-alone program or as a module, component, subroutine, or otherunit suitable for use in a computing environment.

Suitable processors for the execution of a program of instructionsinclude, by way of example, both general and special purposemicroprocessors, and the sole processor or one of multiple processors ofany kind of computer. Generally, a processor will receive instructionsand data from a read-only memory or a random access memory or both. Theessential elements of a computer are a processor for executinginstructions and one or more memories for storing instructions and data.Generally, a computer will also include, or be operatively coupled tocommunicate with, one or more mass storage devices for storing datafiles; such devices include magnetic disks, such as internal hard disksand removable disks; magneto-optical disks; and optical disks. Storagedevices suitable for tangibly embodying computer program instructionsand data include all forms of non-volatile memory, including by way ofexample semiconductor memory devices, such as EPROM, EEPROM, and flashmemory devices; magnetic disks such as internal hard disks and removabledisks; magneto-optical disks; and CD-ROM and DVD-ROM disks. Theprocessor and the memory can be supplemented by, or incorporated in,ASICs (application-specific integrated circuits).

To provide for interaction with a user, the features can be implementedon a computer having a display device such as a CRT (cathode ray tube)or LCD (liquid crystal display) monitor for displaying information tothe user and a keyboard and a pointing device such as a mouse or atrackball by which the user can provide input to the computer.Additionally, such activities can be implemented via touchscreenflat-panel displays and other appropriate mechanisms.

The features can be implemented in a control system that includes aback-end component, such as a data server, or that includes a middlewarecomponent, such as an application server or an Internet server, or thatincludes a front-end component, such as a client computer having agraphical user interface or an Internet browser, or any combination ofthem. The components of the system can be connected by any form ormedium of digital data communication such as a communication network.Examples of communication networks include a local area network (“LAN”),a wide area network (“WAN”), peer-to-peer networks (having ad-hoc orstatic members), grid computing infrastructures, and the Internet.

While this specification contains many specific implementation details,these should not be construed as limitations on the scope of anyinventions or of what may be claimed, but rather as descriptions offeatures specific to particular implementations of particularinventions. Certain features that are described in this specification inthe context of separate implementations can also be implemented incombination in a single implementation. Conversely, various featuresthat are described in the context of a single implementation can also beimplemented in multiple implementations separately or in any suitablesubcombination. Moreover, although features may be described previouslyas acting in certain combinations and even initially claimed as such,one or more features from a claimed combination can in some cases beexcised from the combination, and the claimed combination may bedirected to a subcombination or variation of a subcombination.

Similarly, while operations are depicted in the drawings in a particularorder, this should not be understood as requiring that such operationsbe performed in the particular order shown or in sequential order, orthat all illustrated operations be performed, to achieve desirableresults. In certain circumstances, multitasking and parallel processingmay be advantageous. Moreover, the separation of various systemcomponents in the implementations described previously should not beunderstood as requiring such separation in all implementations, and itshould be understood that the described program components and systemscan generally be integrated together in a single software product orpackaged into multiple software products.

A number of implementations have been described. Nevertheless, it willbe understood that various modifications may be made without departingfrom the spirit and scope of the disclosure. For example, exampleoperations, methods, or processes described in this disclosure mayinclude more steps or fewer steps than those described. Further, thesteps in such example operations, methods, or processes may be performedin different successions than that described or illustrated in thefigures. Accordingly, other implementations are within the scope of thefollowing claims.

What is claimed is:
 1. A method for determining rock properties, comprising: exerting a compressive load with a test apparatus across a rock sample that comprises a specified length-to-diameter ratio; measuring, with a strain gauge, a strain on the rock sample during the compressive loading; determining, based at least in part on the compressive load, a mechanical property of the rock sample; and determining, based at least in part on the measured strain and the compressive load, an elastic property of the rock sample.
 2. The method of claim 1, wherein the specified length-to-diameter ratio is between 0.2 and 0.75.
 3. The method of claim 1, wherein the test apparatus comprises a Brazilian test apparatus.
 4. The method of claim 1, wherein the strain gauge is coupled to an axial surface of the rock sample.
 5. The method of claim 4, wherein measuring a strain on the rock sample during the compressive loading comprises: measuring an incremental axial strain on the rock sample during a compressive load increment with a first strain gauge; and measuring an incremental radial strain on the rock sample during the compressive load increment with a second strain gauge.
 6. The method of claim 5, wherein determining, based at least in part on the measured strain and the compressive load, the elastic property of the rock sample comprises: determining a first coefficient based at least in part on the diameter of the rock sample, the length of the rock sample, and an effective length of the first and second strain gauges; determining a second coefficient based at least in part on the diameter of the rock sample, the length of the rock sample, and the effective length of the first and second strain gauges; and determining the elastic property of the rock sample based at least in part on the measured incremental axial and radial strains on the rock sample, the first and second coefficients, and the compressive loading increment.
 7. The method of claim 5, wherein determining, based at least in part on the measured strain and the compressive load, the elastic property of the rock sample comprises determining a Young's modulus of the rock sample based on at least one of: (i) $\begin{matrix} {{E = {\frac{\Delta \; P}{\Delta \; ɛ_{x}}\left( {{- F} + {vG}} \right)}},} & (i) \end{matrix}$ where E is stress dependent Young's modulus of the rock sample, ΔP is a compressive loading increment, Δε_(x) is an incremental radial strain, ν is Poisson's ratio of the rock sample, F is a first coefficient, and G is a second coefficient; or (ii) $\begin{matrix} {{E = {\frac{\; P}{\; ɛ_{x}}\left( {{- F} + {vG}} \right)}},} & ({ii}) \end{matrix}$ where E is Young's modulus of the rock sample, P is a particular compressive load, ε_(x) is a radial strain at the particular compressive load, ν is Poisson's ratio of the rock sample, F is the first coefficient, and G is the second coefficient.
 8. The method of claim 5, wherein determining, based at least in part on the measured strain and the compressive load, the elastic property of the rock sample comprises determining Poisson's ratio of the rock sample based on at least one of: (i) $\begin{matrix} {{\upsilon = \frac{{\left( \frac{\Delta \; ɛ_{x}}{{\Delta ɛ}_{y}} \right)G} + F}{{\left( \frac{\Delta \; ɛ_{x}}{{\Delta ɛ}_{y}} \right)F} + G}},} & (i) \end{matrix}$ where ν is stress dependent Poisson's ratio of the rock sample, Δε_(x) is an incremental radial strain, Δε_(y) is an incremental axial strain, F is a first coefficient, and G is a second coefficient; or (ii) $\begin{matrix} {{\upsilon = \frac{{\left( \frac{\; ɛ_{x}}{ɛ_{y}} \right)G} + F}{{\left( \frac{\; ɛ_{x}}{ɛ_{y}} \right)F} + G}},} & ({ii}) \end{matrix}$ where u is Poisson's ratio of the rock sample, ε_(x) is a radial strain at a particular compressive load on the rock sample, Δε_(y) is an axial strain at the particular compressive load on the rock sample, F is the first coefficient, and G is the second coefficient.
 9. The method of claim 1, wherein the mechanical property comprises at least one of a tensile strength or a brittleness of the rock sample.
 10. The method of claim 1, wherein the strain gauge comprises a linear variable differential transformer (LVDT).
 11. A rock property test system, comprising: a load cell configured to exert a compressive load across a rock sample; at least one strain gauge positioned to measure a strain on the rock sample during the compressive loading; and a control system communicably coupled to the load cell and the at least one strain gauge and configured to perform operations comprising: controlling the load cell to exert an incremental compressive load on the rock sample; receiving a measured strain on the rock sample, based on the incremental compressive load, from the at least one strain gauge; determining, based at least in part on the incremental compressive load, a mechanical property of the rock sample; and determining, based at least in part on the measured strain and the incremental compressive load, an elastic property of the rock sample.
 12. The rock property test system of claim 11, wherein the rock sample comprises a length-to-diameter ratio between 0.2 and 0.75.
 13. The rock property test system of claim 11, wherein the load cell comprises a Brazilian test apparatus.
 14. The rock property test system of claim 11, wherein the strain gauge is configured to attach to an axial surface of the rock sample.
 15. The rock property test system of claim 14, wherein the strain gauge comprises: a first strain gauge configured to measure an incremental axial strain on the rock sample during the incremental compressive load; and a second strain gauge configured to measure an incremental radial strain on the rock sample during the incremental compressive load.
 16. The rock property test system of claim 15, wherein the control system is configured to perform further operations comprising: determining a first coefficient based at least in part on the diameter of the rock sample, the length of the rock sample, and an effective length of the first and second strain gauges; determining a second coefficient based at least in part on the diameter of the rock sample, the length of the rock sample, and the effective length of the first and second strain gauges; and determining the elastic property of the rock sample based at least in part on the measured incremental axial and radial strains on the rock sample, the first and second coefficients, and the incremental compressive load.
 17. The rock property test system of claim 15, wherein the operation of determining, based at least in part on the measured strain and the compressive load, the elastic property of the rock sample comprises determining a Young's modulus of the rock sample based on at least one of: (i) $\begin{matrix} {{E = {\frac{\Delta \; P}{{\Delta ɛ}_{x}}\left( {{- F} + {vG}} \right)}},} & (i) \end{matrix}$ where E is stress dependent Young's modulus of the rock sample, ΔP is a compressive loading increment, Δε_(x) is an incremental radial strain, ν is Poisson's ratio of the rock sample, F is a first coefficient, and G is a second coefficient; or (ii) $\begin{matrix} {{E = {\frac{P}{ɛ_{x}}\left( {{- F} + {vG}} \right)}},} & ({ii}) \end{matrix}$ where E is Young's modulus of the rock sample, P is a particular compressive load, ε_(x) is a radial strain at the particular compressive load, ν is Poisson's ratio of the rock sample, F is the first coefficient, and G is the second coefficient.
 18. The rock property test system of claim 15, wherein the operation of determining, based at least in part on the measured strain and the compressive load, the elastic property of the rock sample comprises determining Poisson's ratio of the rock sample based on at least one of: (i) $\begin{matrix} {{\upsilon = \frac{{\left( \frac{\Delta \; ɛ_{x}}{{\Delta ɛ}_{y}} \right)G} + F}{{\left( \frac{\Delta \; ɛ_{x}}{{\Delta ɛ}_{y}} \right)F} + G}},} & (i) \end{matrix}$ where ν is stress dependent Poisson's ratio of the rock sample, Δε_(x) is an incremental radial strain, Δε_(y) is an incremental axial strain, F is a first coefficient, and G is a second coefficient; or (ii) $\begin{matrix} {{\upsilon = \frac{{\left( \frac{\; ɛ_{x}}{ɛ_{y}} \right)G} + F}{{\left( \frac{\; ɛ_{x}}{ɛ_{y}} \right)F} + G}},} & ({ii}) \end{matrix}$ where ν is Poisson's ratio of the rock sample, ε_(x) is a radial strain at a particular compressive load on the rock sample, Δε_(y) is an axial strain at the particular compressive load on the rock sample, F is the first coefficient, and G is the second coefficient.
 19. The rock property test system of claim 11, wherein the mechanical property comprises at least one of a tensile strength or a brittleness of the rock sample.
 20. A method, comprising: performing a Brazilian test on a rock sample, the Brazilian test comprising: exerting an incremental compressive load across a rock sample; and determining, based at least in part on the incremental compressive load, a mechanical property of the rock sample; measuring, with a strain gauge, a strain on the rock sample during the incremental compressive load; and determining, based at least in part on the measured strain and the incremental compressive load, an elastic property of the rock sample.
 21. The method of claim 20, wherein the rock sample comprises a disc having a length-to-diameter ratio between 0.2 and 0.75.
 22. The method of claim 20, wherein the strain comprises an axial strain and a radial strain, and determining the elastic property of the rock sample comprises: determining the elastic property of the rock sample based at least in part on the axial and radial strains on the rock sample and the incremental compressive load.
 23. The method of claim 22, wherein determining the elastic property of the rock sample based at least in part on the axial and radial strains on the rock sample and the incremental compressive load comprises: determining the elastic property of the rock sample based at least in part on the axial and radial strains on the rock sample, the incremental compressive load, and two predetermined constants.
 24. The method of claim 23, wherein the two predetermined constants are based at least in part on a diameter of the rock sample, a length of the rock sample, and an effective length of the strain gauge. 